May 22, 2024Open Access

Groups of singular alternating sign matrices

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Abstract

We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs), and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a singular idempotent ASM as its identity element. The relationship between the size, the rank, and the possible multiplicative orders of singular ASMs is explored.

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O'Brien et al. (Wed,) studied this question.

synapsesocial.com/papers/68e68fc0b6db643587617526 https://doi.org/https://doi.org/10.48550/arxiv.2405.13611

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